Question: Define a Hidden Markov model with the following parameters: Three states S = {1, 2, 3} and alphabet A = {a, b, c}, 0 0.5

Define a Hidden Markov model with the following parameters: Three states S = {1, 2, 3} and alphabet A = {a, b, c}, 0 0.5 0.5 P = 0.8 0.2 0 0 1 0 T = OOH b1(a) = 1 b1 ( 6 ) = 3, b1 ( c ) = 0 b2(a) = 7, b2(b) = 0, 62(c) = b3(a) = 0, b3(b) = 7, 63(c) = (a) Find the probability that the state sequence was q = (1, 3, 2) and that the observation sequence was O = (a, b, a). That is, find P(q, O|)). (b) Given that the fifth hidden state was q5 = 2, find the probability that the sixth emitted symbol is 06 = a

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